A 30 cm long organ pipe is filled with air and is open at one end and closed at the other. The speed of sound in air at 0°C is 331 m/s. What is the wavelength of the third mode of vibration?
Question
A 30 cm long organ pipe is filled with air and is open at one end and closed at the other. The speed of sound in air at 0°C is 331 m/s. What is the wavelength of the third mode of vibration?
Solution
To find the wavelength of the third mode of vibration for a pipe that is open at one end and closed at the other, we first need to understand that the fundamental frequency (or first harmonic) of such a pipe is when there is one quarter of a wave inside the pipe.
The second harmonic (or first overtone) is when there are three quarters of a wave inside the pipe, and the third harmonic (or second overtone) is when there are five quarters of a wave inside the pipe.
So, for the third mode of vibration, there are five quarters of a wave inside the pipe.
Step 1: Convert the length of the pipe to meters: 30 cm = 0.3 m
Step 2: Calculate the length of the wave for the third mode of vibration: The length of the pipe is equal to five quarters of the wavelength, so we can set up the equation: 0.3 m = 5/4 * wavelength
Step 3: Solve for the wavelength: wavelength = 0.3 m * 4/5 = 0.24 m
So, the wavelength of the third mode of vibration is 0.24 m.
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